While digital audio recordings provide many advantages over analog systems, the data storage requirements for high-fidelity recordings are substantial. A high fidelity recording typically requires more than one million bits per second of playback time. The total storage needed for even a short recording is too high for many computer applications. In addition, the digital bit rates inherent in non-compressed high fidelity audio recordings makes the transmission of such audio tracks over limited bandwidth transmission systems difficult. Hence, systems for compressing audio sound tracks to reduce the storage and bandwidth requirements are in great demand.
One class of prior an audio compression systems divide the sound track into a series of segments. Over the time interval represented by each segment, the sound track is analyzed to determine the signal components in each of a plurality of frequency bands. The measured components are then replaced by approximations requiring fewer bits to represent, but which preserve features of the sound track that are important to a human listener. At the receiver, an approximation to the original sound track is generated by reversing the analysis process with the approximations in place of the original signal components. 
The analysis and synthesis operations are normally carried out with the aid of perfect, or near perfect, reconstruction filter banks. The systems in question include an analysis filter bank which generates a set of decimated subband outputs from a segment of the sound track. Each decimated subband output represents the signal in a predetermined frequency range. The inverse operation is carried out by a synthesis filter bank which accepts a set of decimated subband outputs and generates therefrom a segment of audio sound track. In practice, the synthesis and analysis filter banks are implemented on digital computers which may be general purpose computers or special computers designed to more efficiently carry out the operations. If the analysis and synthesis operations are carried out with sufficient precision, the segment of audio sound track generated by the synthesis filter bank will match the original segment of audio sound track that was inputted to the analysis filter bank. The differences between the reconstructed audio sound track and the original sound track can be made arbitrarily small. In this case, the specific filter bank characteristics such as the length of the segment analyzed, the number of filters in the filter bank, and the location and shape of filter response characteristics would be of little interest, since any set of filter banks satisfying the perfect, or near-perfect, reconstruction condition would exactly regenerate the audio segment. 
Unfortunately, the replacement of the frequency components generated by the analysis filter bank with a quantized approximation thereto results in artifacts that do depend on the detail characteristics of the filter banks. There is no single segment length for which the artifacts in the reconstructed audio track can be minimized. Hence, the length of the segments analyzed in prior art systems is chosen to be a compromise. When the frequency components are replaced by approximations, an error is introduced in each component. An error in a given frequency component produces an acoustical effect which is equivalent to the introduction of a noise signal with frequency characteristics that depend on filter characteristics of the corresponding filter in the filter bank. The noise signal will be present over the entire segment of the reconstructed sound track. Hence, the length of the segments is reflected in the types of artifacts introduced by the approximations. If the segment is short, the artifacts are less noticeable. Hence, short segments are preferred. However, if the segment is too short, there is insufficient spectral resolution to acquire information needed to properly determine the minimum number of bits needed to represent each frequency component. On the other hand, if the segment is too long, temporal resolution of the human auditory system will detect artifacts. 
Prior art systems also utilize filter banks in which the frequency bands are uniform in size. Systems with a few (16-32) sub-bands in a 0-22 kHz frequency range are generally called “subband coders” while those with a large number of sub-bands (.gtoreq.64) are called “transform coders”. It is known from psychophysical studies of the human auditory system that there are critical bandwidths which vary with frequency. The information in a critical band may be approximated by a component representing the time averaged signal amplitude in the critical band. 
In addition, the ear's sensitivity to a noise source in the presence of a localized frequency component such as a sine tone depends on the relative levels of the signals and on the relation of the noise spectral components to the tone. The errors introduced by approximating the frequency components may be viewed as “noise”. The noise becomes significantly less audible if its spectral energy is within one critical bandwidth of the tone. Hence, it is advantageous to use frequency decompositions which approximate the critical band structure of the auditory system. 
Systems which utilize uniform frequency bands are poorly suited for systems designed to take advantage of this type of approximation. In principle, each audio segment can be analyzed to generate a large number of uniform frequency bands, and then, several bands at the higher frequencies could be merged to provide a decomposition into critical bands. This approach imposes the same temporal constraints on all frequency bands. That is, the time window over which the low frequency data is generated for each band is the same as the time window over which each high-frequency band is generated. To provide accuracy in the low frequency ranges, the time window must be very long. This leads to temporal artifacts that become audible at higher frequencies. Hence, systems in which the audio segment is decomposed into uniform sub-bands with adequate low-frequency resolution cannot take full advantage of the critical band properties of the auditory system. 
Prior art systems that recognize this limitation have attempted to solve the problem by utilizing analysis and synthesis filter banks based on QMF filter banks that analyze a segment of an audio sound track to generate frequency components in two frequency bands. To obtain a decomposition of the segment into frequency components representing the amplitudes of the signal in critical bands, these two frequency band QMF filters are arranged in a tree-structured configuration. That is, each of the outputs of the first level filter becomes the input to another filter bank at least one of whose two outputs is fed to yet another level, and so on. The leaf nodes of this tree provide an approximation to a critical band analysis of the input audio track. It can be shown that this type of filter bank used different length audio segments to generate the different frequency components. That is, a low frequency component represents the signal amplitude in an audio segment that is much longer than a high-frequency component. Hence, the need to choose a single compromise audio segment length is eliminated. 
While tree structured filter banks having many layers may be used to decompose the frequency spectrum into critical bands, such filter banks introduce significant aliasing artifacts that limit their utility. In a multilevel filter bank, the aliasing artifacts are expected to increase exponentially with the number of levels. Hence, filter banes with large numbers of levels are to be avoided. Unfortunately, filter banks based on QMF filters which divide the signal into two bandlimited signals require large numbers of levels. 
Prior art audio compression systems are also poorly suited to applications in which the playback of the material is to be carried out on a digital computer. The use of audio for computer applications is increasingly in demand. Audio is being integrated into multimedia applications such as computer based entertainment, training, and demonstration systems. Over the course of the next few years, many new personal computers will be outfitted with audio playback and recording capability. In addition, existing computers will be upgraded for audio with the addition of plug-in peripherals. 
Computer based audio and video systems have been limited to the use of costly outboard equipment such as an analog laser disc player for playback of audio and video. This has limited the usefulness and applicability of such systems. With such systems it is necessary to provide a user with a highly specialized playback configuration, and there is no possibility of distributing the media electronically. However, personal computer based systems using compressed audio and video data promise to provide inexpensive playback solutions and allow distribution of program material on digital disks or over a computer network. 
Until recently, the use of high quality audio on computer platforms has been limited due to the enormous data rate required tier storage and playback. Quality has been compromised in order to store the audio data conveniently on disk. Although some increase in performance and some reduction in bandwidth has been gained using conventional audio compression methods, these improvements have not been sufficient to allow playback of high fidelity recordings on the commonly used computer platforms without the addition of expensive special purpose hardware.
One solution to this problem-would be to use lower quality playback on computer platforms that lack the computational resources to decode compressed audio material at high fidelity quality levels. Unfortunately, this solution requires that the audio material be coded at various quality levels. Hence, each audio program would need to be stored in a plurality of formats. Different types of users would then be sent the format suited to their application. The cost and complexity of maintaining such multi-format libraries makes this solution unattractive. In addition, the storage requirements of the multiple formats partially defeats the basic goal of reducing the amount of storage needed to store the audio material. 
Furthermore, the above discussion assumes that the computational resources of a particular playback platform are fixed. This assumption is not always true in practice. The computational resources of a computing system are often shared among a plurality of applications that are running in a time-shared environment. Similarly, communication links between the playback platform and shared storage facilities also may be shared. As the playback resources change, the format of the audio material must change in systems utilizing a multi-format compression approach. This problem has not been adequately solved in prior art systems. 
In prior art multi-carrier systems, a communication path having a fixed bandwidth is divided into a number of sub-bands having different frequencies. The width of the sub-bands is chosen to be the same for all sub-bands and small enough to allow the distortion in each sub-band to be modeled by a single attenuation and phase shift for the band. If the noise level in each band is known, the volume of data sent in each band may be maximized for any given bit error rate by choosing a symbol set for each channel having the maximum number of symbols consistent with the available signal-to-noise ratio of the channel. By using each sub-band at its maximum capacity, the amount of data that can be transmitted in the communication path for a given error rate is maximized.
For example, consider a system in which one of the sub-channels has a signal-to-noise ratio which allows at least 16 digital levels to be distinguished from one another with an acceptable error rate. In this case, a symbol set having 16 possible signal values is chosen. If the incoming data stream is binary, each consecutive group of 4 bits is used to compute the corresponding symbol value which is then sent on the communication channel in the sub-band in question.
In digitally implemented multi-carrier systems, the actual synthesis of the signal representing the sum of the various modulated carriers is carried out via a mathematical transformation that generates a sequence of numbers that represents the amplitude of the signal as function of time. For example, a sum signal may be generated by applying an inverse Fourier transformation to a data vector generated from the symbols to be transmitted in the next time interval. Similarly, the symbols are recovered at the receiver using the corresponding inverse transformation.
The computational workload inherent in synthesizing and analyzing the multi-carrier signal is related to the number of sub-bands. For example, if Fourier transforms are utilized, the workload is of order NlogN where N is the number of sub-bands. Similar relationships exist for other transforms. Hence, it is advantageous to minimize the number of sub-bands.
There are two factors that determine the number of sub-bands in prior art systems. First, the prior art systems utilize a uniform bandwidth. Hence, the number of sub-bands is at least as great as the total bandwidth available for transmission divided by the bandwidth of the smallest sub-band. The size of the smallest sub-band is determined by need to characterize each channel by a single attenuation and phase shift. Thus, the sub-band having the most rapidly varying distortion sets the number of sub-bands and the computational workload in the case in which white noise is the primary contributor to the signal-to-noise ratio.
In systems in which the major source of interference is narrow band interference, the minimum sub-band is set with reference to the narrowest sub-band that must be removed from the communication channel to avoid the interference. Consider a communication channel consisting of a twisted pair of wires which is operated at a total communication band which overlaps with the AM broadcast band in frequency. Because of the imperfect shielding of the wires, interference from strong radio stations will be picked up by the twisted pair. Hence, the sub-bands that correspond to these radio signals are not usable. In this case, prior art systems break the communication band into a series of uniform sub-bands in which certain sub-bands are not used. Ideally, the sub-bands are sufficiently narrow that only the portion of the spectrum that is blocked by a radio signal is lost when a sub-band is marked as being unusable.
Broadly, it is the object of the present invention to provide an improved multi-carrier transmission system.
It is a further object of the present invention to provide a multi-carrier transmission system having a lower computational workload than imposed by systems having bands of equal band-width.
These and other objects of the present invention will become apparent to those skilled in the art from the following detailed description of the invention and the accompanying drawings.